The invention concerns a broadband ellipsometer/polarimeter system and a method of polarimetric measurement of Mueller matrices.
Ellipsometry is a non-destructive characterization technique that measures the change in polarization state of light reflected (or transmitted) by a sample.
The present ellipsometric/polarimetric system contains an excitation section emitting a light beam. Said light beam passes through a polarisation state generator (PSG) and is focused on the sample. After being transmitted, reflected or scattered by the sample, the beam goes through an analysis section containing a polarisation state analyser (PSA) and a detection means.
Such PSG and PSA (which is also called PSD (polarisation state detector)) are described in the document US2004130717.
In a PSG, the light polarization can be modulated by a variety of devices such as discrete components inserted and then removed from the light path {Bickel W. S. et al.; Am. J. Phys 53 (1984) 468}, rotating retardation plates {Goldstein D. H.; Appl. Opt. 31 (1992) 6676}, rotating compensators {Collins R. W. and Koh J.; J. Opt. Soc. A 16, (1999) 1997}, Pockels cells {Delplancke F.; Appl. Opt. 36 (1997) 5388 and Compain E. and Drévillon B.; Rev. Sci. Instrum. 68 (1997) 2671} or photoacoustic modulators {Compain E. and Drévillon B.; Rev. Sci. Instrum. 69, (1998) 1574}.
For PSA, one can use the same devices and a single detector, or a “parallel” analysis of light polarization through polarization-sensitive beamsplitters and simultaneous measurement of the separated beams by several detectors {Azzam R. M. A., Opt. Acta 29 (1982) 685, Brudzewski K.; J. Modern Optics 38 (1991) 889, Khrishnan S.; J. Opt. Soc. Am A 9 (1992) 1615, Compain E. et al., Thin Solid Films 313 (1998)}.
The optical set-up is completed with appropriate optics to collimate the beam into the PSG and into the PSA, and to focus the beam onto the sample surface and on the detector. The PSG generates a set of four independent states of polarization, which after being transformed by the sample, are projected over the PSA to be analyzed. The PSA produces a set of four independent optical configurations to analyze the polarization of the light emerging from the sample for each state that was previously created by the PSG. As a result, a complete measurement run yields a set of 16 independent values that eventually, allows the calculation of the sample Mueller matrix or ellipsometric angles.
To date, several ellipsometers/polarimeters have been described, most of them working in the ultraviolet—visible (UV-VIS) wavelength range (250 to 900 nm) and only a small number working in the mid infrared (IR) (4 to 20 microns) or in the far ultraviolet (FUV) (140 nm-250 nm). This fact can be roughly explained because typically optical elements perform better in the UV-VIS than in the IR of the FUV and also because even though the visible spectral range is relatively narrow, it appears to be sufficient for some applications. However, there is an increasing interest in expanding the measured spectra because FUV and IR have particular advantages. The IR gives unique information about the chemical bonding within a sample, which is inaccessible to the sole UV-VIS. Moreover, because of its longer wavelengths, the IR, is less sensitive than the UV-VIS to surface structures (roughness, inhomogeneity among others). It is also better suited to the analysis of thick films (>several microns) that usually make the interpretation of conventional measurements difficult. On the other hand, the shortness of the FUV wavelengths make it ideal to measure the thickness of very thin films (<a few nm), in addition, the enhanced sensitivity of FUV to small defects and structures in the surface of samples is used for surface state quality control. Finally, it is of general agreement that the wider the measured spectral range, the better is the reliability of the final results.
The preceding arguments prove the necessity for an apparatus providing ellipsometric/polarimetric measurements in spectral ranges as wide as possible. Two particular interesting ranges are the IR range from 4 to 20 microns, and the FUV-NIR from 140 nm to 2 microns.
Briefly, the disclosed apparatus uses polarizers and retarders to create and to analyze the polarization state of a radiation beam. This apparatus is operated by placing the retarders at a set of 16 different orientations with respect to the polarizers, which are kept still.
In order to work in optimal conditions over all the measured spectral range, the polarizers and the retarders used in the instrument must be as much achromatic as possible. The operation mode of the disclosed ellipsometer/polarimeter system imposes an additional constraint to the design of the retarders. They must not deviate the beam even when they are rotated about an axis defined by the direction of the beam. Even if substantially achromatic polarizers can eventually be found commercially this is not always the case for substantially achromatic retarders.
An article of Benett et al. {Appl. Opt., (1970)}, has been used as a reference to select the most adapted types and characteristics of the retarders to be used in the disclosed ellipsometer/polarimeter system. In said article, Bennett et al., compare the optical performances of low order, zero order and total internal reflection (TIR) based retarders. The conclusion is that, even though TIR retarders are more sensitive to the beam alignment and aperture than the low order and zero order plates, they seem to be the optimum choice to be integrated into wide range spectroscopic systems because of their enhanced achromatism.
Concerning achromatic retarders, an article of Oxley {Phil. Mag., (1911)} has been considered because it gives some insight on the manufacture of two types of TIR based quarter wave retarders that do not deviate the beam when they are rotated. One of them is a V-shaped retarder made of two Fresnel rhombs, called bi-prism. The bi-prism geometry has become popular because of the easiness of construction and high achromaticity.
A patent of Thomson et al. {U.S. Pat. No 5,706,212}, describes an infrared ellipsometer/polarimeter system using pseudo-achromatic retarders. Each one of said retarders consists of a bi-prism cut to a given angle in order to create a total retardation of ¾λ. In a preferred embodiment, the ellipsometer has two retarders located respectivelly before and after the sample. During current operation of the ellipsometer/polarimeter, each retarder is rotated to a minimum of nine 9 azimuthal angle settings leading to at least eighty one 81 different raw data acquisitions. These acquisitions are then decomposed in terms of a double discrete Fourier series. From the coefficients of the said Fourier series, it is possible to calculate the characteristic Mueller matrix of the sample and of the optical components of the ellipsometer/polarimeter.